What version of Premiere Elements and what computer operating system are involved?
If you have Premiere Elements 11 and earlier, then you first step is to go to an opened project and use Help Menu/Deactivate to Deactivate the program. Close out of there. At this point, you can leave the deactivated program as is or continue on to uninstall it. Deactivation and Uninstall are not the same thing. To keep your "allowable" count of same purchased activated serial number on no more than 2 of your computers, Deactivation does it.
In Premiere Elements 12 and 13, for deactivation, the Help Menu/Deactivate is now Help Menu/Sign Out.
Any questions, do not hesitate to ask.